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TT-Toolbox (TT=Tensor Train) Version 2.2.2

TT(Tensor Train) format is an efficient way for low-parametric representation of high-dimensional tensors. The TT-Toolbox is a MATLAB implementation of basic operations with tensors in TT-format. It includes:

  • tt_tensor and tt_matrix classes for storing vectors and operators
  • Basic linear algebra subroutines (addition, matrix-by-vector product, elementwise multiplication and many others) using standard MATLAB syntax, linear complexity in the dimension, reshape function
  • Fast rounding procedure with a prescribed accuracy
  • Advanced approximation and solution techniques:
  • Approximate solution of linear systems and eigenvalue problems
  • Cross methods to approximate ``black-box'' tensors
  • Wavelet tensor train decomposition
  • Construction of basic operators and functions (Laplace operator, function of a TT-tensor)
  • Computation of maximal and minimal elements of a tensor
  • and several others

New in Version 2.2.2

  • one-element MATLAB-style subsref and subsassgn now possible for tt_matrix: current_value=ttm(123,4567) and ttm(123,4567)=new_value
  • submatrix extraction is now possible: ttm2=ttm([1 2 7],[1 2 1;1 1 2]) For additional help see code of @tt_matrix/subsref.m and core/tt_submatrix.m

New in Version 2.2.1

  • Blockwise assembly of tt_matrices added: ttM=tt_blockwise({ttA ttB ttC;ttD ttE ttF})
  • subtensor extraction is now possible: ttv2=ttv(1,2,:,2,2,:,:,:,1) or ttv2=ttv({1,2,':',2,2,':',':',':',1}) For additional help see code of @tt_tensor/subsref.m and core/tt_subtensor.m

New in Version 2.2

  • Better documentation
  • Mixed QTT-Tucker format (qtt_tucker class)
  • reshape function for a TT-tensor/TT-matrix
  • dmrg_cross method for black-box tensor approximation
  • Convolution in QTT-format